DiscreteRiccatiSolve[{a, b}, {q, r}] gives the matrix x that is the stabilizing solution of the discrete algebraic Riccati equation ConjugateTranspose[a].x.a - x - ...

Mathematica includes functionality to factor polynomials symbolically.

A linear second-order ordinary differential equation is said to be exact if An exact linear second-order ODE is solved by reduction to a linear first-order ODE.

For most differential equations, the results given by NDSolve are quite accurate. However, because its results are based on numerical sampling and error estimates, there can ...

The systems of equations that govern certain phenomena (in electrical circuits, chemical kinetics, etc.) contain a combination of differential equations and algebraic ...

If the given second-order ODE is inhomogeneous, DSolve applies the method of variation of parameters to return a solution for the problem. This solves an inhomogeneous linear ...

SolveAlways[eqns, vars] gives the values of parameters that make the equations eqns valid for all values of the variables vars.

Mathematica's approach to differential operators provides both an elegant and a convenient representation of mathematical structures, and an immediate framework for strong ...

If you have an equation like 2x==0, it is perfectly clear that the only possible solution is x->0. However, if you have an equation like ax==0, things are not so clear. If a ...